Sauce: Whisk cornstarch with chicken stock until smooth, then stir in the remaining sauce ingredients and set aside.
Since cooking goes quickly, prep everything first. Finely dice the onion, carrot, mushrooms, and pepper. Mince the garlic & ginger. Drain and finely dice the water chestnuts. Thinly slice green onions.
Heat oil in a large skillet over medium-high heat. Add onion, garlic, & ginger. Cook for 2-3 minutes until fragrant and starting to soften. Add the ground chicken and break it up with a wooden spoon. Cook for 5-7 minutes, stirring often, until mostly cooked through. If there is any excess liquid, drain it and return the skillet to medium high heat.
Add carrot, red pepper, mushrooms, & water chestnuts. Cook for 2-3 minutes until the carrot softens. Give the sauce a quick stir, then pour it into the skillet. Cook for 1-2 minutes until thickened and evenly coating the filling. Taste and adjust seasoning, adding salt if needed.
Transfer filling to a serving bowl. Spoon into lettuce leaves and top with green onions and optional chopped nuts. Serve with lime wedges and squeeze fresh lime over the wraps before eating. Enjoy right away.
Video
Notes
Storage: The filling tastes even better the next day! Store the filling and lettuce in separate containers in the fridge. Keep garnishes like nuts and lime stored separately.